Optical transmission systems are used to transmit data in different types of systems such as telecommunication systems. Optical communication systems provide larger transmission capacities than wired or wireless communication systems. From access networks to metropolitan and long-haul networks, optical transmission technologies can carry data over long distances with low attenuations. They have become a key technology of modern telecommunication infrastructures.
During the last decade, the continuous growth in the number of connected machines and users as well as the emergence of multimedia applications and services have accelerated the demand for higher transmission data rates and hence the development of optical transmission systems which use optical fibers as optical transmission lines.
Such developments have been driven by the multiple degrees of freedom offered by the optical fibers. Optical fibers enable multiplexing more data channels and the introduction of new digital signal processing techniques that mitigate the impairments of the channel while guaranteeing a reliable communication with the highest achievable rates.
Several degrees of freedom are used in existing optical transmission systems such as amplitude, phase and polarization states of the optical field, time and wavelength.
Early optical communication systems were based on single-mode fibers. Optical-fiber transmission systems were based on an “On-Off” modulation of the intensity of light along with non-coherent detection. Such approach requires a low amount of optical components at low costs. However, it only takes advantage of the amplitude of the optical field.
To further exploit the phase of the optical field, coherent detection was introduced. Coherent detection enables the detection of both the amplitude and the phase of signals, thereby enabling the use of higher-order modulation formats and an increase of the capacity of optical fiber links.
In addition to coherent detection, optical amplifiers were also proposed to enable the transmission of independent modulated wavelength without opto-electrical regeneration as disclosed in “P. J. Winzer, High-Spectral-Efficiency Optical Modulation Formats, In Journal of Lightwave Technology, vol. 30, no. 24, pp. 3824-3835, December 2012”. Such technique is known as Wavelength Division Multiplexing (WDM).
Coherent detection can double the capacity of an optical link by using the two orthogonal polarization states of the optical field. Using Polarization Division Multiplexing (PDM) techniques, independent data symbols can be sent over the two polarization states of the optical signal. As a result, the spectral efficiency of the optical transmission system can be also doubled.
On top of the various degrees of freedom offered by single-mode fibers, multi-mode fibers give access to an extra degree of freedom, so-called ‘space’ which stems from the availability of several propagation modes. A propagation mode defines the distribution of a wave while propagating in the fiber. Multi-mode fibers allow the propagation of many modes in a single-core or multi-core fibers where each core can be single-mode or multi-mode. The various propagation modes form a set of orthogonal channels over which independent data symbols can be multiplexed using Space Division Multiplexing (SDM) techniques. SDM in multi-mode fibers can enable a multiplication of the capacity of a link by the number of propagation modes.
Space remains the only available degree of freedom that can be used in optical transmission to meet the demand for more network capacity, since all the other degrees of freedom (namely frequency, time, phase, and polarization) are already exploited to satisfy the demand for bandwidth. There is accordingly a need to develop optical fiber transmission systems combining WDM, PDM, and SDM techniques that provide a support of higher capacities for example for access networks, metropolitan networks and long-haul terrestrial and transoceanic links, taking into account all available degrees of freedom of multi-mode fibers.
The multiplexing of independent data symbols over the various available degrees of freedom requires managing numerous impairments and crosstalk between the various multiplexing channels. Such impairments can deteriorate the performance of the transmission system. In both PDM and SDM systems, loss disparities between the channels are essentially due to imperfections of the optical components (e.g. fibers, amplifiers and multiplexers) and to crosstalk effects between the propagation modes in multi-mode fibers. Such imperfections induce non-unitary impairments, i.e. impairments that cause a loss of orthogonality and/or a loss of energy between the different channels over which independent data symbols are multiplexed. Such impairments can significantly reduce the capacity of the optical links.
Non-unitary effects in PDM systems, known as polarization dependent loss (PDL), have been addressed in “E. Awwad, Y. Jaouën, G. Rekaya-Ben Othman, E. Pincemin, Polarization-Time Coded OFDM for PDL mitigation in long-haul optical transmission systems, European Conference and Exhibition on Optical Communication (ECOC), P.3.4, London—UK, September 2013”. Signal processing solutions combining Orthogonal Frequency Division Multiplexing (OFDM) with Polarization-Time Coding that provide efficient mitigation of PDL effects in PDM systems have been proposed. The developed Polarization-Time coding techniques are based on Space-Time codes, initially constructed for multiplexing data in wireless communication systems using multiple antenna technologies. Solutions exist for performing multi-carrier modulation through the use of OFDM for a low-complexity implementation of the Polarization-Time codes.
Non-unitary effects in SDM systems known as mode dependent loss (MDL), have been studied from both the optical and signal processing perspectives. Optical solutions using mode scrambling or strong mode coupling were proposed to reduce the impact of MDL on the channel capacity. For example, a technique based on placing mode scramblers between the fiber spans is disclosed in “A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, B. Lankl, Mode Scramblers and Reduced-Search Maximum-Likelihood Detection for Mode-Dependent-Loss-Impaired Transmission, In the Proceedings of the European Conference and Exhibition on Optical Communication, September 2013”. This technique enables the reduction of the MDL effect. However, it fails to completely mitigate MDL and requires a high number of scramblers.
The use of existing Space-Time codes comprising the Silver code, the Golden code and the Alamouti code for PDL mitigation have paved the way for investigating their possible potential for MDL mitigation in SDM systems. Digital signal processing solutions based on Space-Time coding for MDL mitigation in SDM systems were explored in recent works disclosed in “E. Awwad, G. Rekaya-Ben Othman, Y. Jaouën, and Y. Frignac, Space-Time Codes for Mode-Multiplexed Optical Fiber Transmission Systems, OSA Advanced Photonics Congress: Signal Processing for Photonic Communications (SPPCom), San Diego—USA, July 2014”. Such approach was focused on SDM systems involving 3 and 6 propagation modes for different values of modal dispersion loss and revealed the promising potential of the use of Space-Time codes for a complete MDL mitigation at low costs.
The Space-Time codes used for MDL mitigation in existing approaches are codes that were essentially designed for wireless communication systems where signals carrying data symbols undergo Rayleigh fading-like attenuations. Although optical-fiber transmission systems can be represented as multiple-input multiple-output systems, the optical fiber propagation environment differs from the wireless medium. Existing Space-Time codes may not be accordingly sufficiently adapted to optical MIMO (for Multiple-Input Multiple-Output) systems, in particular to SDM systems. There is accordingly a need for digital coding techniques enabling a complete mitigation of MDL effects for SDM systems.